Finitary incidence algebras.

Abstract

Let P be an arbitrary partially ordered set and I(P) its incidence space. Then F(P) is the finitary incidence algebra and I(P) is a bimodule over it. Consequently we can form D(P) = FI(P) ⊕ I(P) the idealization of I(P). In this paper we will study the automorphisms of FI(P) and D(P). We will also explore sufficient conditions for FI(P) to be zero product determined.